Method for Determining the Modulus of Elasticity of Paper

ABSTRACT

In a method for determining the radial modulus of elasticity of paper or a corresponding web-like material that can be reeled or wound on a reel, the connection between the force and deflection of a material arranged in layers is measured. The measurements of force and deflection necessary for calculating the radial modulus of elasticity are performed on a reel of paper or corresponding material outside the reeling or winding position by loading the reel with a press member.

CROSS REFERENCES TO RELATED APPLICATIONS

This application is a U.S. national stage application of internationalApp. No. PCT/FI2003/000784, filed Oct. 22, 2003, the disclosure of whichis incorporated by reference herein. This application claims priority onFinnish App. No. 20021902, filed Oct. 24, 2002.

STATEMENT AS TO RIGHTS TO INVENTIONS MADE UNDER FEDERALLY SPONSOREDRESEARCH AND DEVELOPMENT

Not applicable.

BACKGROUND OF THE INVENTION

The present invention relates to a method for determining the radialmodulus of elasticity of paper or a corresponding web-like material thatcan be reeled or wound on a reel. In said method the connection betweenthe force and deflection of a material arranged in superimposed layersis measured.

A known method for measuring the radial modulus of elasticity of paperis a measurement conducted in a laboratory, which is disclosed forexample in the publication by D. Roisum: The Mechanics of Winding, TappiPress 1994, p. 62. The measurement is conducted in such a manner that astack of paper sheets is pressed between two planes. As a result of themeasurement a curve is attained, which represents the pressing force asa function of the height of the stack. The stress is obtained bydividing the force by the measurement area. The strain of the paperstack, which in this case is, in fact, compression, is obtained bydividing the change in the height by the original height of the stack.The paper stack is loaded until it reaches such stress which issubstantially the same as the maximum stress that is assumed to beeffective inside the reel. The loading of the paper stack is conductedseveral times in succession. The radial modulus of elasticity is theslope of the tangent of the stress-strain curve.

It is a problem of the laboratory measurement that it is conducted witha delay, in other words reactions to problems in the production occurslowly. The shape of the paper stack does not entirely correspond to theshape of the reel in the production machine. Furthermore, it isnecessary to use a paper stack, wherein it is somewhat difficult toprepare a sample for the measurement. In this measurement it is,however, necessary to use a paper stack, because it is very difficult tomeasure single sheets and it may cause inaccurate results.

SUMMARY OF THE INVENTION

By means of the method according to the invention it is possible toeliminate or reduce the above-mentioned problems. The method accordingto the invention is characterized in that the measurements of force anddeflection that are necessary in the determination of the radial modulusof elasticity are performed on a paper reel outside the reeling orwinding position. The term reeling or winding position refers to theposition in which the reel is located when material in the form of acontinuous web is reeled or wound thereon.

The advantages of the method according to the invention are that themeasurement of force and deflection can be performed on the reel,wherein the shape of the surface to be measured is correct. By means ofthe measurement, information is obtained which indicates how the reelingor winding should be conducted, for example which web tension should beutilized at a given time, in other words, the measurement results can beapplied in theoretical winding models. Because the measurements are madeon the finished reel, it is possible to rapidly react to errors in thereeling or winding. Inaccurately reeled or wound material can be reeledagain or rejected. The method according to the invention can be appliedafter the reeling or winding position of reel-ups or winders of varioustypes, such as center winders or carrier drum winders when the reel hasbeen transferred to a special measurement position. The method can alsobe applied in a corresponding manner in continuously operated reel-ups.

When the aim is to use theoretical winding models to attain windingparameter recipes, it is necessary to know the constitutive behavior ofthe paper reel, i.e. the connection between the stress and strain of thepaper reel. When an elastic orthotropic plane model is used, fourvariables are necessary for describing this connection, of whichvariables the radial modulus of elasticity is dependent on the pressureinside the reel and the other three variables are typically assumed tobe constant. A method has now been developed for estimation of theradial modulus of elasticity, which method will be describedhereinbelow.

When the method according to the invention is used, the measurements offorce and deflection necessary in the calculation of the radial modulusof elasticity of paper or a corresponding material are conducted outsidethe reeling or winding position of paper or a corresponding material, inother words the reel is transferred from the reeling or winding positionto a special measurement position. In the measurement a stationary(non-rotating) paper reel or the like is loaded with forces of differentmagnitude in the direction of the radius of the paper reel, anddeflections corresponding to the forces are registered. In thisapplication, the term deflection refers to the compression of layeredpaper or corresponding material on a reel in the direction of the radiusof the reel when the reel is loaded with a force in the direction of thereel radius. The compression can be measured either directly from themovement of the press member in the radial direction of the reel, orindirectly from the extent of the contact area in the loading (theextent of the contact area in the direction of the periphery of the reelcorrelates with the deflection).

The measurement is conducted when the paper reel or the like ispositioned in a measurement station which comprises means for producingand registering the deflection, and means for registering the forcecorresponding to the deflection. The measurement is conducted after thepaper reel is finished, the reel is stopped and transferred thereafterto the measurement station. The reel is loaded with a known force and atthe same time the deflection of the reel is measured. The member loadingthe reel in the measurement station can be a press member pressing thesurface of the reel by means of a pivotal movement or linear movement.The measurement of the deflection can be conducted for example bymeasuring this movement, or the deflection-dependent extent of thecontact area between the straight surface of the loading member and thesurface of the paper reel in the loading situation. The force can bemeasured by means of a sensor placed in the press member, or on thebasis of the force required by the loading movement. On the basis of themeasurement result a curve is obtained showing the deflection in thedirection of the radius of the reel as a function of the force loadingthe reel.

The deflections are determined using the same press member withdifferent force values, wherein several pairs of measurement results(measurement points) of force and deflection are obtained. Their numberis so large that it is possible to obtain a reliable force-deflectioncurve by means of them. In practice, it is possible to increase theforce constantly, and measure the forces and the correspondingdeflection at sufficiently short intervals or constantly, when the pressmember is pressed constantly towards the central axis of the reel in thedirection of the radius.

The tangential modulus of elasticity of paper or corresponding web-likematerial to be reeled or wound, obtained as a measurement result eitheras a laboratory measurement or in the production machine, is placed inthe theoretical loading model of the paper reel. Elastic parameters usedas initial guesses are also necessary in the theoretical loading model.On the basis of the theoretical loading model another curve is obtaineddescribing the deflection in the direction of the radius of the reel asa function of the force loading the reel.

The theoretical loading model of the paper reel can be for example amodel utilizing FEM (finite element model) calculation. FEM calculationis known as such and therefore it will not be described in more detail.Generally, it can be said that the FEM calculation is utilized when theuse of exact mathematical formulas is difficult for example due to theircomplex nature.

The curve obtained on the basis of the measurement results and the curveobtained on the basis of the theoretical loading model are compared toeach other. If they match, the initial guess of the elastic parametersis correct. If the curves do not match, new values are given for theelastic parameters, and this process continues until the curve obtainedby means of the theoretical loading model corresponds to the measurementresults. The radial modulus of elasticity becomes entirely known forexample from the elastic parameters that have been initially included inthe calculation as guesses. On the basis of the obtained result it ispossible to estimate the radial modulus of elasticity. In the estimationit is possible to use for example the least squares method in which aminimum of the square of the difference of the calculated and measuredvalues is sought.

In the following, the invention will be described by means of drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows the method according to the invention in a block diagram.

FIGS. 2 and 3 show, in side-views of the reel, some measurement stationsin which it is possible to carry out the method according to theinvention.

FIG. 4 shows a preferred embodiment of the method in a front view of thereel.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIG. 1 shows the method according to the invention for measuring theradial modulus of elasticity of paper in a block diagram. To calculatethe radial modulus of elasticity, an initial guess of the elasticparameters and a tangential modulus of elasticity measured from thepaper are necessary.

The radial modulus of elasticity can be represented with the formulaE_(r)=E_(r)(σ_(r)), i.e. E_(r) depends on the radial stress σ_(r). Thisdependency can be described with a 1^(st) to 3^(rd) order polynom.Elastic parameters which are required as initial guesses can be forexample the coefficients of this polynom.

The tangential modulus of elasticity can be measured by means oflaboratory measurement, or it can be measured in the production machine.When the elastic parameters given as an initial guess are placed in thetheoretical reeling model, and a curve of the compression of the reel asa function of the nip load is obtained as a result of the FEMcalculation, the obtained curve is compared with the curve representingthe deflection of the reel as a function of the nip load, obtained fromthe production machine as a measurement result. If the curves match, theinitial guess is correct. If they do not match, new values are given forthe elastic parameters and the comparison of the curves continues.

FIG. 2 illustrates the measurement conducted after the slitter winder.The measurement is conducted in the measurement station, for exampleafter a WinBelt® winder or a WinRoll™ winder. The measurement stationcan be placed in a location to which the rolls are transferred next fromthe winder, for example at the location of the supporting base followingthe winding position, onto which base the roll is rolled from the top ofthe carrier drum and stopped.

FIG. 2 shows a first principle of the method according to the invention,in which a customer roll R wound around a core in the slitter winder ispressed from above by means of a press member 1 positioned at the end ofa pivotal arm 2. The arm is arranged pivotable in the vertical plane,and it is attached to a suitable frame structure. The arm 2 is presseddown and at the same time the press member 1 is pressed against the rollR with a force device F arranged between the frame and the arm 2. Theangular position of the loading arm 2 (angle θ) is measured by means ofan angular sensor 4. By means of the angle and the force produced by theforce device 3 it is possible to determine the depression of the pressmember 1 as a function of the radial force produced by the press member1.

The force device 3 can be for example a hydraulic cylinder that producesa force that can be measured and on the basis of the same it is possibleto calculate the force produced by the press member 1.

The press member 1 can be relatively small, but it is a prerequisite forits function that it does not change its form in the loading. The pressmember 1 can be made of steel or another suitably hard material. Thelower surface of the press member is planar and the plane is positionedapproximately tangentially with respect to the peripheral surface of thereel.

In order to be able to measure the actual loading force accurately, itis possible to utilize a suitable force sensor 5 on the lower surface ofthe press member 1. This force sensor measures directly the nip forceeffective in the nip between the surface of the force member 1 and theperipheral surface of the roll R. It is possible to use for example apressure sensitive film sensor that is capable of giving a measurementsignal proportional to the force. One example is a piezoresistivemeasurement film or a corresponding film sensor. By using a largesurface film sensor or several sensors at different locations of thepress member 1, it is also possible to measure the shape of the nip,i.e. the contact width, by means of which more information can beobtained. The contact width, i.e. the extent of the contact area in thedirection of the periphery of the roll also indicates the deflection,wherein by means of a suitable sensor arrangement of the press member itis possible to measure both the force and the deflection.

FIG. 3 shows another method in which a press member 1 is also positionedat the end of an arm 2. The function is analogous with FIG. 2, with thedistinction that the force device 3 produces a linear movement, becausethe press member 1 and the arm 2 are arranged to move linearly in aguide. Also in this case it is possible to determine the force on thebasis of the force used by the force device 3 or the force sensor 5placed in the press member 1. To measure the movement proportional tothe deflection, it is in this alternative possible to utilize asufficiently accurate sensor 4 capable of measuring the linear movement.In this alternative it is also possible to determine the deflection bymeans of the sensor of the press member, if it can be utilized todetermine the extent of the contact area.

In the measurement position of both FIG. 2 and 3, the roll R has beentransferred away from the winding position. The measurement stationcomprises a measurement base 6 on which the roll is located sufficientlywell supported from below, its rolling being prevented. The supportingbase 6 can be located for example on the floor level. It is an advantageof performing the measurement outside the reel-up or winder that themeasurement can be conducted without disturbing the reeling or windingprocess. When the measurement is conducted in a station in which therolls are normally discharged when their winding is complete, thesequence of the set change of the winder will not be disturbed either.Since it is possible to wind a new roll in the winder at the same timewhen the roll R is measured in the measurement station, the windingprocess will not be disturbed and measurements can be conducted inprinciple until the roll must be transferred away from the path of thenext roll coming from the winding process, said roll being the next oneto be measured in the same measurement station.

FIG. 4 shows yet another advantageous embodiment. The press member 1 isarranged to move in the cross direction, i.e. in the axial direction ofthe roll (longitudinal direction of the core), wherein it is possible todetermine the force-deflection curve at different locations of the roll.The curves measured at different locations can be used for measuring thecross-directional profile of the radial module of the roll. In practice,the measurement station of FIG. 4 is implemented in such a manner thatthe press member 1 is arranged movable on a guide 7 extending in thecross direction, from which guide the arm 2 supporting the press member1 can be suspended by fastening it for example to a carriage 8 or thelike moving back and forth in the longitudinal direction of the guide.

The arrangement of FIG. 4 can also be utilized for measuring severaladjacent rolls, which situation occurs when several rolls wound from thesame web after the slitting operation is taken out of the reel-winder.The press member 1 is transferred successively on top of each reel. Oneach roll, it is possible to measure one point or several points todetermine a profile.

The above-mentioned examples of the embodiments do not restrict theinvention. The method according to the invention can also be applied incontinuously operating reel-ups that are arranged to reel a paper web ofproduction width on consecutive machine reels. Such a measurement can beconducted for is example when the machine reel is located outside thereeling position on reeling rails, or when the machine reel ispositioned in the unwinder, before its unwinding begins. It is alsopossible to determine a profile for the machine reel. The main idea inthis invention is that the measurements of force and deflectionnecessary in the calculation of the radial modulus of elasticity ofpaper or a corresponding material can be performed directly on a reelwithout disturbing the reeling or winding process, and thus thelaboratory measurement stage that causes extra work can be omitted.

1-10. (canceled)
 11. A method for determining a radial modulus ofelasticity of a paper web or a corresponding web-like material, whichcan be reeled or wound on a reel, in which method the connection betweenthe force and deflection of a web material arranged in layers ismeasured, wherein the method comprises the steps of: reeling or windingthe web material to form a reel in a reeling or winding position, thereel defining a reel axis and a radial direction toward the reel axis;transferring the reel from the reeling or winding position to ameasurement position; and making measurements of force and deflection soas to allow calculating the radial modulus of elasticity of the reel ofthe web material in the measurement position outside the reeling orwinding position.
 12. The method of claim 11, wherein the reel of webmaterial is loaded with a force in the radial direction which ispredetermined, and deflection of the reel in the radial direction thatcorresponds to the force is measured and registered.
 13. The method ofclaim 12, wherein while the reel of web material is being loaded withthe predetermined force, a curve is obtained of the deflection of thereel in the radial direction as a function of the force.
 14. The methodof claim 13, wherein the curve obtained is compared to a theoreticallycalculated curve of deflection of the reel in the radial direction as afunction of the force.
 15. The method of claim 14, wherein when thetheoretically calculated curve of deflection of the reel in the radialdirection as a function the force corresponds to the curve obtained fromthe measurement results, the radial modulus of elasticity is estimatedfrom elastic parameters that have been used in calculating thetheoretically calculated curve of deflection.
 16. The method of claim12, wherein the reel is loaded with a planar surface of a press membermoving in the radial direction toward the reel axis.
 17. The method ofclaim 16, wherein the force is measured by a force sensor positioned inthe press member loading the reel and the force sensor being in contactwith the reel.
 18. The method of claim 17, wherein the force sensor isalso utilized to determine a loaded area extent on the reel.
 19. Themethod of claim 18, wherein the deflection of the reel in the radialdirection is determined on the basis of the loaded area extent on thereel.
 20. The method of claim 19, wherein the deflection of the reel inthe radial direction is determined on the basis of the loaded areaextent on the reel.
 21. The method of the claim 12, wherein the force ismeasured by a force sensor positioned in a press member loading the reeland the force sensor being in contact with the reel.
 22. The method ofclaim 21, wherein the force sensor is also utilized to determine aloaded area extent on the reel.
 23. The method of claim 11, wherein aprofile of the radial modulus of elasticity of the web material isdetermined by performing a force and a deflection measurement atdifferent points in the axial direction of the reel.
 24. The method ofclaim 23, wherein the profile is measured by moving a press member in anaxial direction of the reel and performing the force and the deflectionmeasurements at the different points with the press member.
 25. Themethod of claim 11, wherein the radial modulus of elasticity of the webmaterial is determined by performing a force and a deflectionmeasurement on different adjacent reels by transferring a press membersuccessively on top of said adjacent reels.
 26. The method of claim 11,wherein the web material is paper.
 27. A method for determining a radialmodulus of elasticity of a paper web that can be reeled or wound on areel, in which method the connection between the force and deflection ofthe paper web arranged in layers in the reel is measured, wherein themethod comprises the steps of: reeling or winding the paper web to forma reel in a reeling or winding position, the reel defining a reel axisand a radial direction toward the reel axis; transferring the reel fromthe reeling or winding position to a measurement position; and makingmeasurements of force and deflection so as to allow calculating theradial modulus of elasticity of the reel of the paper web in themeasurement position outside the reeling or winding position.
 28. Themethod of claim 27, wherein a profile of the radial modulus ofelasticity of the paper web is determined by performing a force and adeflection measurement at different points in the axial direction of thereel.
 29. The method of claim 28, wherein the profile is measured bymoving a press member in an axial direction of the reel and performingthe force and the deflection measurements at the different points withthe press member.
 30. The method of claim 27, wherein the radial modulusof elasticity of the paper web is determined by performing a force and adeflection measurement on different adjacent reels by transferring apress member successively on top of said adjacent reels.